If you were doing a stainless sink, I would say to do a stainless strainer, even with a copper faucet. But, since you are doing the cast iron, I would match the faucet. I'm not sure if they are compatible, but Rohl makes white strainers to go with their fireclay sinks. You could try that too.

White strainer is an option; I would check w/Kohler to see what they have as options and/or with your plumber/installer. You could pull in the copper perhaps with a copper sink grid in your white sink- functional and love the extra copper to coordinate w/faucet.

White would be an option as well... but are they as durable? That's the thing I keep coming back to. I do like that option with a copper grid if they have such a thing. Thanks!

We have a solid copper drain/strainer if interested. Most on the market are plated and the plating wears off in a year or so.